Is the initial size really as large as the final size, though? I would think not. Perhaps we can get GiC in here to analyze this. I was thinking more along the lines of...

I think you're looking for something more along the lines of:

ex+(c/2)*erf(-x)+c/2

where c is a constant that is equal to the asymptote on the left and erf is the Gaussian error function. Feel free to play with the coefficients to give it the exact shape and location relative to the x and y axes you want.